The plasma relaxed state for the coaxial helicity injection current drive in toroidal configuration is investigated by applying the principle of minimum rate of energy dissipation. The comparison between theory and helicity injection current drive experiment on HIT (the Helicity Injected Tokamak) [T. R. Jarboe, Fusion Technol. 15, 7 (1989)] is presented. The calculation results indicate that the key features such as total toroidal driven current, current in closed field, current density profile, magnetic configuration, and j(t)/B-t profile agree quite well with experiment. Analysis shows that plasma relaxes to a noncomplete relaxation state, and the toroidal current is effectively driven in this state. (C) 1998 American Institute of Physics.